Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
arXiv:1201.4578 · doi:10.1088/0953-4075/45/5/055302
Abstract
We consider the three-dimensional (3D) mean-field model for the Bose-Einstein condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes the sign of the nonlinearity along the axial direction, and the harmonic-oscillator trapping potential applied in the transverse plane. The lattice can be created as an optical or magnetic one, by means of available experimental techniques. The objective is to identify stable 3D solitons supported by the setting. Two methods are developed for this purpose: The variational approximation, formulated in the framework of the 3D Gross-Pitaevskii equation, and the 1D nonpolynomial Schrödinger equation (NPSE) in the axial direction, which allows one to predict the collapse in the framework of the 1D description. Results are summarized in the form of a stability region for the solitons in the plane of the NL strength and wavenumber. Both methods produce a similar form of the stability region. Unlike their counterparts supported by the NL in the 1D model with the cubic nonlinearity, kicked solitons of the NPSE cannot be set in motion, but the kick may help to stabilize them against the collapse, by causing the solitons to shed excess norm. A dynamical effect specific to the NL is found in the form of freely propagating small-amplitude wave packets emitted by perturbed solitons.
14 pages, 8 figures. To be published in J. Phys. B: At. Mol. Opt. Phys
References in corpus (18)
- Tuning the scattering length with an optically induced Feshbach resonance
- Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
- Spontaneous symmetry breaking in a nonlinear double-well structure
- Deviation from one-dimensionality in stationary properties and collisional dynamics of matter-wave solitons
- Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
- Fully three dimensional breather solitons can be created using Feshbach resonance
- Vector solitons in nearly-one-dimensional Bose-Einstein condensates
- Stable two-dimensional solitons in nonlinear lattices
- Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
- Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
- Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices
- Matter-wave solitons with a periodic, piecewise-constant nonlinearity
- Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates
- Bose-Einstein condensates under a spatially-modulated transverse confinement
- Interlaced linear-nonlinear optical waveguide arrays
- Effective one-dimensional dynamics of elongated Bose-Einstein condensates
- Matter-wave 2D solitons in crossed linear and nonlinear optical lattices
- Quantum phase transition of Bose-Einstein condensates on a ring nonlinear lattice
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- Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
- Solitons in a Hamiltonian -symmetric coupler
- Accurate one-dimensional effective description of realistic matter-wave gap solitons
- Symmetry Breaking in Bose-Einstein Condensates Confined by a Funnel Potential